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the transport protocol behaves in ``extreme'' ways for example, minimal or no congestion control it is possible for the protocol stack to exert suf cient in uence such that the transfer mechanism of causality is signi cantly impeded. 20 and its discussion of multifractal IP traf c with different scaling behavior at small and large time scales, where the multiplicative scaling at small time scales at roughly sub-RTT times is taken to stem from the actions associated with TCP's feedback congestion control, can be viewed as a re ned characterization of the in uence of the protocol stack, in this case, for short-term correlation structure of network traf c. In 15, Feldmann presents an empirical study of the characteristics of TCP connection arrivals and shows that in today's Internet, in addition to self-similarity at the packet level, self-similar scaling is already encountered at the session or application layer when analyzing time series of the number of TCP connections per time unit. To this end, Feldmann relies on wavelet-based inference techniques and uncovers that various facets of TCP connection arrival characteristics conform to Weibullian-type distributions. This detailed workload characterization is relevant from both traf c modeling and control perspectives since knowing the structure of TCP connection arrivals and their durations can help in devising improved traf c control mechanisms. The chapter by Roberts ( 16) gives a high-level discussion of traf c control and resource provisioning issues under long-range dependent traf c conditions. The basic premise is predicated on segmenting traf c into two broad classes stream and elastic traf c where the former are subjected to open-loop control, that is, resource reservation, and the latter are handled using closed-loop control. Due to the heavy queueing cost associated with provisioning resources using buffer sizing, it is explicitly proposed that for stream traf c, bandwidth allocation with small buffer capacity be the default resource allocation policy employed. Roberts sketches the components of a multiservice network architecture advocating measurementbased admission control for stream traf c considered effective for self-similar traf c, and end-to-end feedback control for elastic traf c, with pricing applicable to both. The in uence of self-similarity and heavy tailedness on architectural considerations and traditional traf c control are discussed throughout. In 17, Duf eld and Whitt adopt a bufferless model for performance analysis and traf c control where instantaneous offered load is given by a long-term level process (i.e., ``DC'' component shifts across a range of traf c levels) with ``within-level'' uctuations. They investigate the problem of approximating the conditional mean of aggregate traf c conditioned on past traf c pro le or demand parameterized by level and age (or duration) using numerical transform inversion. They show that the age variable plays an important role in facilitating prediction. Duf eld and Whitt show applications of the ``transient analysis framework'' by estimating the probability of high levels of congestion in steady state using a large deviation principle approximation. They also analyze the converse situation captured by the time to recover that is, return to a traf c level corresponding to a given resource capacity after the excursion. The approach advanced in 17 is interesting due to its focus on the long-range dependent aggregate input process,
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dispensing with its impact on queueing, and directly analyzing the transient or dynamic variability structure based on the predictability inherent to long-range dependent processes. A similar ``on-line'' framework is adopted in 18 where long-term predictability structure is exploited for feedback congestion control. Tuan and Park ( 18) show that in spite of the ``bad news'' associated with scale-invariant burstiness, there is ``good news'' in the sense of there being the potential of exploiting long-term correlation structure present in long-range dependent traf c for traf c control purposes. They advance the multiple time scale congestion control framework and show that nonnegligible correlations at large time scales can be effectively detected on-line and engaged to improve the performance of feedback congestion controls in rate-based settings. The central idea underlying the technology is selective aggressiveness control, which allows explicit prediction of large time scale network state to be used to modulate the aggressiveness of bandwidth consumption behavior exhibited by feedback congestion control acting at small time scales (i.e., time scale of RTT). An important consequence is the mitigation of the delay bandwidth product problem of reactive controls in broadband wide-area networks. Finally, 19 by Adas and Mukherjee addresses the problem of how resource reservation in a time-division multiplexing set up per-VC framing can be used to facilitate end-to-end quality of service (QoS) under long-range dependent traf c conditions. The asynchronous framing approach described follows the resource provisioning paradigm espoused for long-range dependent traf c, namely, that of bufferless queueing, which then allows computation of QoS guarantees by appealing to the central limit theorem and equivalent bandwidth computations. REFERENCES
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1. P. Abry and D. Veitch. Wavelet analysis of long-range dependent traf c. IEEE Trans. Information Theory, 44(1):2 15, 1998. 2. A. Adas and A. Mukherjee. On resource management and QoS guarantees for long range dependent traf c. In Proc. IEEE INFOCOM '95, pp. 779 787, 1995. 3. R. Addie, M. Zukerman, and T. Neame. Fractal traf c: measurements, modelling and performance evaluation. In Proc. IEEE INFOCOM '95, pp. 977 984, 1995. 4. G. Amdahl. Validity of the single-processor approach to achieving large scale computing capabilities. In AFIPS Conf. Proc., pp. 483 485, 1967. 5. V. Anantharam. Queueing analysis with traf c models based on deterministic dynamical systems. In Proc. 25th Allerton Conference on Communication, Control and Computing, pp. 233 241, 1996. 6. M. Arlitt and C. Williamson. Internet Web servers: workload characterization and performance implications. IEEE=ACM Trans. Networking, 5(5):631 645, 1997. 7. P. Barford and M. Crovella. Generating representative workloads for network and server performance evaluation. In Proc. ACM SIGMETRICS '98, pp. 151 160, 1998. 8. M. Barnsley. Fractals Everywhere. Academic Press, New York, 1988.
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